date: _______________ bell: ______ homework 3: quiz 1 review
directions: name all sets of numbers to which each real number belongs.
1. $-\frac{14}{2}$ 2. $\sqrt{64}$ 3. $0$
4. $\pi$ 5. $0.\overline{45}$ 6. $\frac{3}{8}$
directions: place the letter of each value in its location in the real number system below.
a. $-0.\overline{2}$ b. $18$ c. $-\sqrt{100}$ d. $\pi$ e. $0$ f. $2\frac{1}{6}$ g. $-5$ h. $4.03$ i. $-\sqrt{50}$ j. $\sqrt{\frac{4}{9}}$ k. $\frac{36}{9}$
venn diagram: irrational (circle), rational (circle with nested integers, whole, natural circles)

Question

date: _______________ bell: ______ homework 3: quiz 1 review
directions: name all sets of numbers to which each real number belongs.
1. $-\frac{14}{2}$  2. $\sqrt{64}$  3. $0$
4. $\pi$  5. $0.\overline{45}$  6. $\frac{3}{8}$
directions: place the letter of each value in its location in the real number system below.
a. $-0.\overline{2}$  b. $18$  c. $-\sqrt{100}$  d. $\pi$  e. $0$  f. $2\frac{1}{6}$  g. $-5$  h. $4.03$  i. $-\sqrt{50}$  j. $\sqrt{\frac{4}{9}}$  k. $\frac{36}{9}$
venn diagram: irrational (circle), rational (circle with nested integers, whole, natural circles)

Accepted Answer

### Problem 1: $-\frac{14}{2}$
# Explanation:
## Step 1: Simplify the fraction
Simplify $-\frac{14}{2}$: $-\frac{14}{2} = -7$.
## Step 2: Identify number sets
- **Integers**: Integers include all whole numbers and their negatives (..., -3, -2, -1, 0, 1, 2, 3, ...). -7 is an integer.
- **Rational Numbers**: A rational number is any number that can be expressed as a fraction $\frac{a}{b}$ where $b
eq 0$. Since $-7 = \frac{-7}{1}$, it is rational.
- **Real Numbers**: All integers and rational numbers are real numbers. So -7 is a real number.
# Answer: Integers, Rational Numbers, Real Numbers

### Problem 2: $\sqrt{64}$
# Explanation:
## Step 1: Simplify the square root
Simplify $\sqrt{64}$: $\sqrt{64} = 8$.
## Step 2: Identify number sets
- **Natural Numbers**: Natural numbers are positive integers (1, 2, 3, ...). 8 is a natural number.
- **Whole Numbers**: Whole numbers include 0 and all natural numbers (0, 1, 2, 3, ...). 8 is a whole number.
- **Integers**: Integers include all whole numbers and their negatives. 8 is an integer.
- **Rational Numbers**: 8 can be written as $\frac{8}{1}$, so it is rational.
- **Real Numbers**: 8 is a real number.
# Answer: Natural Numbers, Whole Numbers, Integers, Rational Numbers, Real Numbers

### Problem 3: $0$
# Explanation:
## Step 1: Identify number sets
- **Whole Numbers**: Whole numbers include 0 and positive integers. 0 is a whole number.
- **Integers**: Integers include all whole numbers and their negatives. 0 is an integer.
- **Rational Numbers**: 0 can be written as $\frac{0}{1}$, so it is rational.
- **Real Numbers**: 0 is a real number.
# Answer: Whole Numbers, Integers, Rational Numbers, Real Numbers

### Problem 4: $\pi$
# Explanation:
## Step 1: Recall the definition of $\pi$
$\pi$ is a non - repeating, non - terminating decimal (approximately 3.1415926...).
## Step 2: Identify number sets
- **Irrational Numbers**: A number that cannot be expressed as a fraction $\frac{a}{b}$ (where $a$ and $b$ are integers and $b
eq0$) is irrational. Since $\pi$ has a non - repeating, non - terminating decimal expansion, it is irrational.
- **Real Numbers**: All irrational numbers are real numbers. So $\pi$ is a real number.
# Answer: Irrational Numbers, Real Numbers

### Problem 5: $0.\overline{45}$ (0.454545...)
# Explanation:
## Step 1: Recall the definition of rational numbers
A repeating decimal can be expressed as a fraction. Let $x = 0.\overline{45}$, then $100x=45.\overline{45}$. Subtract $x$ from $100x$: $100x - x=45.\overline{45}-0.\overline{45}$, $99x = 45$, so $x=\frac{45}{99}=\frac{5}{11}$.
## Step 2: Identify number sets
- **Rational Numbers**: Since $0.\overline{45}$ can be expressed as a fraction $\frac{5}{11}$, it is rational.
- **Real Numbers**: All rational numbers are real numbers. So $0.\overline{45}$ is a real number.
# Answer: Rational Numbers, Real Numbers

### Problem 6: $\frac{3}{8}$
# Explanation:
## Step 1: Recall the definition of rational numbers
A number in the form $\frac{a}{b}$ (where $a$ and $b$ are integers and $b
eq0$) is rational. Here $a = 3$ and $b = 8$ (both integers, $b
eq0$).
## Step 2: Identify number sets
- **Rational Numbers**: $\frac{3}{8}$ is a rational number.
- **Real Numbers**: All rational numbers are real numbers. So $\frac{3}{8}$ is a real number.
# Answer: Rational Numbers, Real Numbers

### Placing values in the real number system:
#### Irrational (numbers that cannot be expressed as a fraction):
- $D. \pi$: $\pi$ is non - repeating, non - terminating.
- $I. -\sqrt{50}$: $\sqrt{50}=5\sqrt{2}$, and $\sqrt{2}$ is irrational, so $-\sqrt{50}$ is irrational.

#### Rational (numbers that can be expressed as a fraction):
- **Integers (a subset of rational numbers, whole numbers and their negatives)**:
    - $B. 18$: Positive integer.
    - $C. -\sqrt{100}=- 10$: Negative integer.
    - $E. 0$: Integer.
    - $G. - 5$: Negative integer.
    - $K. \frac{36}{9}=4$: Positive integer.
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Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 1: $-\frac{14}{2}$

Step 1: Simplify the fraction

Step 2: Identify number sets

Step 1: Simplify the square root

Step 2: Identify number sets

Step 1: Identify number sets

Answer:

Problem 2: $\sqrt{64}$